{
 "cells": [
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   "source": [
    "# 2. 线性代数（基于Python）\n",
    "各位同学大家好，欢迎大家来到《线性代数》的世界，上一章《高等数学》我们讨论了许多研究函数的工具，说到底，函数相对是一个连续的世界. 然而事实上，现实世界有很多事情不是连续的，例如当我们拍了一张照片，如果把我们看着是连续变化的图像在电脑上不断放大，你会发现其实是有一个个非常小的像素格组成的，这就是我们在计算中经常使用的一种近似方法，将连续的事物离散化，方便计算机计算.所以在这门课中，我们会讲述离散世界的研究工具，向量、矩阵等等，那我们就开始我们今天的课程吧！\n",
    "\n",
    "本章的主要内容如下：\n",
    "\n",
    "1. 理论知识：\n",
    "- 线性方程组与向量\n",
    "- 向量空间、矩阵、行列式以及范数\n",
    "- 对角化、矩阵的特征值与特征向量、正交化\n",
    "\n",
    "2. 实战案例：\n",
    "- Ginger的智慧农场I——图像的基本处理\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "64e799d9",
   "metadata": {},
   "source": [
    "### 2.1 线性方程组与向量\n",
    "<div class=\"alert alert-info\" role=\"alert\">\n",
    "❓ GitModel 公司的实习生Ginger自己在家中后院组建了一个智慧农场，养了几只公鸡和兔子，由于刚来实习，还不会很深的模型，采用的摄像头对动物计数时候，只能统计有多少个头，有多少只脚.现在摄像头采集到的数据是一共有10个头，28只脚，请问鸡兔各有几只？\n",
    "</div>\n",
    "我们可以列出一个二元一次方程，假设鸡有$x$只，兔子有$y$只那么可以得到\n",
    "\n",
    "$$\n",
    "\\left\\{\\begin{array}{l}\n",
    "x+y=10 \\\\\n",
    "2x+4y=28\n",
    "\\end{array}\\right.\\label{eq1}\n",
    "$$\n",
    "\n",
    "#### 2.1.1 线性方程组\n",
    "$(\\ref{eq1})$在中学阶段叫做二元一次方程组，当然解这个方程组很简单，答案是：$\\left\\{\\begin{array}{l}x=6 \\\\ y=4\\end{array}\\right.$.\n",
    "现在我们忘记中学阶段解二元一次方程组的高斯消元法，把二元一次方程组的本质抽象出来，探讨一种解决二元一次方程组的方法.通过观察，我们发现：二元一次方程组的未知数的阶数都是一次，式子两边都是用等式相连，因此我们给这个方程组起另一个名字：**线性方程组**.在前面的线性方程组中，事实上可以看成是一张表格，\n",
    "\n",
    "| $x$的系数 | $y$的系数 | 结果 |\n",
    "|:---------:|:---------:|:----:|\n",
    "|     1     |     1     |  10  |\n",
    "|     2     |     4     |  28  |\n",
    "\n",
    "我们把同一个未知数的系数放在一起，并且每个变量的系数都用一个**向量**表示，如把$x$的系数放在一起，就是$\\left[\\begin{array}{l}1\\\\2\\end{array}\\right]$,类似的，我们把$y$的系数也放在一起，得到$\\left[\\begin{array}{l}1\\\\4\\end{array}\\right]$. 最后，如果我们把所有数值都移到等式的左边，使得方程组中每个等式右边都为零，那么结果事实上可以看成是$1$的系数，称为常数项，如果我们也放在一起，得到$\\left[\\begin{array}{l}10\\\\28\\end{array}\\right]$.最终，我们的方程组$(\\ref{eq1})$可以用向量形式表示成\n",
    "\n",
    "$$\n",
    "\\left\\{\\begin{array}{l}\n",
    "x+y=10\\\\\n",
    "2x+4y=28\n",
    "\\end{array}\\right.\n",
    "\\Rightarrow\n",
    "\\begin{bmatrix}\n",
    "{1}\\\\\n",
    "{2}\\\\\n",
    "\\end{bmatrix}\n",
    "x+\\begin{bmatrix}\n",
    "{1}\\\\\n",
    "{4}\\\\\n",
    "\\end{bmatrix}\n",
    "y = \\begin{bmatrix}\n",
    "{10}\\\\\n",
    "{28}\\\\\n",
    "\\end{bmatrix}\\label{eq*}\n",
    "$$\n",
    "\n",
    "如果我们将前面包含未知数的两个向量拼接在一起，可以得到一个二维的数表\n",
    "$$\\begin{bmatrix}\n",
    "{1\\quad1}\\\\\n",
    "{2\\quad4}\\\\\n",
    "\\end{bmatrix}$$\n",
    "像这样的数表我们以后将其称为**矩阵**，由于在方程组中，这个矩阵表示的是未知数的系数，故称为系数矩阵，常用$\\mathbf{A}$表示.结果向量也称为常数向量，通常记作$b$.\n",
    "\n",
    "下面我们尝试使用python解线性方程组，```Numpy```中已经封装了求解线性方程组的函数，我们仅需要传入对应的系数矩阵$\\mathbf{A}$以及常数向量$b$，程序就会算出相应的结果."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "caed8718",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-05-27T13:35:36.844186Z",
     "start_time": "2022-05-27T13:35:34.502255Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "线性方程组的解为：\n",
      " [6. 4.]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np \n",
    "A = np.array([[1, 1],\n",
    "              [2, 4]])     # 将系数所有向量拼在一起\n",
    "b = np.array([10,\n",
    "              28])  # 常数向量\n",
    "x = np.linalg.solve(A,b)   # 解线性方程组\n",
    "print(\"线性方程组的解为：\\n\",x)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "44e5f67d",
   "metadata": {},
   "source": [
    "## 2.2 向量空间、矩阵、行列式以及范数"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3bd71d1d",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-05-18T13:15:28.811386Z",
     "start_time": "2022-05-18T13:15:28.801157Z"
    }
   },
   "source": [
    "<div class=\"alert alert-info\" role=\"alert\">\n",
    "❓ 然而，Ginger希望多养几种动物，近日他又引入了几只公鸡和几只鸭子，现在采集到的数据是一共有14个头，40只脚，请问鸡兔鸭各有几只？\n",
    "</div>\n",
    "\n",
    "假设鸭子的数目是$z$只，我们直接列出方程组\n",
    "$$\n",
    "\\left\\{\\begin{array}{l}\n",
    "x + y + z = 14 \\\\\n",
    "2x+4y + 2z = 40\n",
    "\\end{array}\\right.\\label{eq2}\n",
    "$$\n",
    "\n",
    "我们直接采用Python求解："
   ]
  },
  {
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   "execution_count": 2,
   "id": "7f09a2b7",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-05-27T13:35:37.969175Z",
     "start_time": "2022-05-27T13:35:36.848144Z"
    }
   },
   "outputs": [
    {
     "ename": "LinAlgError",
     "evalue": "Last 2 dimensions of the array must be square",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mLinAlgError\u001b[0m                               Traceback (most recent call last)",
      "\u001b[1;32m~\\AppData\\Local\\Temp/ipykernel_1744/1764143189.py\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      3\u001b[0m b = np.array([14,\n\u001b[0;32m      4\u001b[0m               40])  # 常数向量\n\u001b[1;32m----> 5\u001b[1;33m \u001b[0mx\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mlinalg\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msolve\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mA\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mb\u001b[0m\u001b[1;33m)\u001b[0m   \u001b[1;31m# 解线性方程组\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      6\u001b[0m \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"线性方程组的解为：\\n\"\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m<__array_function__ internals>\u001b[0m in \u001b[0;36msolve\u001b[1;34m(*args, **kwargs)\u001b[0m\n",
      "\u001b[1;32mD:\\conda3\\envs\\ML38\\lib\\site-packages\\numpy\\linalg\\linalg.py\u001b[0m in \u001b[0;36msolve\u001b[1;34m(a, b)\u001b[0m\n\u001b[0;32m    378\u001b[0m     \u001b[0ma\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0m_\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0m_makearray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    379\u001b[0m     \u001b[0m_assert_stacked_2d\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 380\u001b[1;33m     \u001b[0m_assert_stacked_square\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    381\u001b[0m     \u001b[0mb\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mwrap\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0m_makearray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mb\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    382\u001b[0m     \u001b[0mt\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mresult_t\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0m_commonType\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mb\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\conda3\\envs\\ML38\\lib\\site-packages\\numpy\\linalg\\linalg.py\u001b[0m in \u001b[0;36m_assert_stacked_square\u001b[1;34m(*arrays)\u001b[0m\n\u001b[0;32m    201\u001b[0m         \u001b[0mm\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mn\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0ma\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    202\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mm\u001b[0m \u001b[1;33m!=\u001b[0m \u001b[0mn\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 203\u001b[1;33m             \u001b[1;32mraise\u001b[0m \u001b[0mLinAlgError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'Last 2 dimensions of the array must be square'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    204\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    205\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0m_assert_finite\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0marrays\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mLinAlgError\u001b[0m: Last 2 dimensions of the array must be square"
     ]
    }
   ],
   "source": [
    "A = np.array([[1, 1, 1],\n",
    "              [2, 4, 2]])     # 将系数所有向量拼在一起\n",
    "b = np.array([14,\n",
    "              40])  # 常数向量\n",
    "x = np.linalg.solve(A,b)   # 解线性方程组\n",
    "print(\"线性方程组的解为：\\n\",x)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ebc2fd02",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger\" role=\"alert\">\n",
    "这个代码一定会报错！它的报错原因说，一定要求系数矩阵是个方阵，这是因为要确定的求解一个多元方程组，有多少个未知数，就需要有多少个方程！所以系数矩阵一定是个方阵.\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "43fc6856",
   "metadata": {},
   "source": [
    "那么，如果我们加入动物眼睛的统计数据，方程组可以为：\n",
    "\n",
    "$$\n",
    "\\left\\{\\begin{array}{l}\n",
    "x + y + z = 14 \\\\\n",
    "2x+4y + 2z = 40 \\\\\n",
    "2x + 2y + 2z = 28\n",
    "\\end{array}\\right.\\label{eq5}\n",
    "$$\n",
    "我们现在再去看每个变量的系数向量，实际上被推广到了三阶，当实际生活中动物越来越多时，我们需要引入的变量也越来越多，所以我们需要引入更高维度的向量来表达我们的问题.一般地，我们研究的问题，变量的个数都是有限的，所以我们一般研究的向量都是有限维的向量，一般称为**n维向量**.\n",
    "\n",
    "继续使用python求解$\\eqref{eq5}$的问题"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "50c88627",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-05-27T13:35:53.998162Z",
     "start_time": "2022-05-27T13:35:53.967269Z"
    }
   },
   "outputs": [
    {
     "ename": "LinAlgError",
     "evalue": "Singular matrix",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mLinAlgError\u001b[0m                               Traceback (most recent call last)",
      "\u001b[1;32m~\\AppData\\Local\\Temp/ipykernel_1744/4287143981.py\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      5\u001b[0m               \u001b[1;36m40\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      6\u001b[0m               28])  # 常数向量\n\u001b[1;32m----> 7\u001b[1;33m \u001b[0mx\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mlinalg\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msolve\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mA\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mb\u001b[0m\u001b[1;33m)\u001b[0m   \u001b[1;31m# 解线性方程组\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      8\u001b[0m \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"线性方程组的解为：\\n\"\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m<__array_function__ internals>\u001b[0m in \u001b[0;36msolve\u001b[1;34m(*args, **kwargs)\u001b[0m\n",
      "\u001b[1;32mD:\\conda3\\envs\\ML38\\lib\\site-packages\\numpy\\linalg\\linalg.py\u001b[0m in \u001b[0;36msolve\u001b[1;34m(a, b)\u001b[0m\n\u001b[0;32m    391\u001b[0m     \u001b[0msignature\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;34m'DD->D'\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0misComplexType\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mt\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32melse\u001b[0m \u001b[1;34m'dd->d'\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    392\u001b[0m     \u001b[0mextobj\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mget_linalg_error_extobj\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0m_raise_linalgerror_singular\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 393\u001b[1;33m     \u001b[0mr\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mgufunc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mb\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0msignature\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0msignature\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mextobj\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mextobj\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    394\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    395\u001b[0m     \u001b[1;32mreturn\u001b[0m \u001b[0mwrap\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mr\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mastype\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult_t\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcopy\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mFalse\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\conda3\\envs\\ML38\\lib\\site-packages\\numpy\\linalg\\linalg.py\u001b[0m in \u001b[0;36m_raise_linalgerror_singular\u001b[1;34m(err, flag)\u001b[0m\n\u001b[0;32m     86\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     87\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0m_raise_linalgerror_singular\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0merr\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mflag\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 88\u001b[1;33m     \u001b[1;32mraise\u001b[0m \u001b[0mLinAlgError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"Singular matrix\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     89\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     90\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0m_raise_linalgerror_nonposdef\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0merr\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mflag\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mLinAlgError\u001b[0m: Singular matrix"
     ]
    }
   ],
   "source": [
    "A = np.array([[1, 1, 1],\n",
    "              [2, 4, 2],\n",
    "              [2, 2, 2]])     # 将系数所有向量拼在一起\n",
    "b = np.array([14,\n",
    "              40,\n",
    "              28])  # 常数向量\n",
    "x = np.linalg.solve(A,b)   # 解线性方程组\n",
    "print(\"线性方程组的解为：\\n\",x)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "15dce4ac",
   "metadata": {},
   "source": [
    "发现事实上还是报错，只不过这次报错的原因是```Singular matrix```，意思是系数矩阵是**奇异的**，或者说是**退化的**.如果观察方程组$\\eqref{eq3}$，你会发现其实第三个式子是第一个式子的2倍导出的，如果我们采用高斯消元法求解方程，那么将式子1的-2倍加到第3个式子，第三个式子就为0了.这说明我们新增的这个式子对于解方程实际上起不到任何作用的，因为它的信息已经被囊括在第一个式子中了.\n",
    "\n",
    "于是现在我们需要解决的问题有两个：\n",
    "1. 当求解n个未知数时，方程组要满足什么条件，才是有解的？\n",
    "2. 当我们将向量推广到高维之后，向量之间的计算是满足的吗？"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1ba38e3c",
   "metadata": {},
   "source": [
    "### 2.2.1 向量的运算法则\n",
    "从上面的方程组改写成向量的表达形式时，大家心中也许会想问一个问题：这两种写法是等价的吗？我们看$\\eqref{eq*}$的计算过程：\n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "{1}\\\\\n",
    "{2}\\\\\n",
    "\\end{bmatrix}\n",
    "x+\\begin{bmatrix}\n",
    "{1}\\\\\n",
    "{4}\\\\\n",
    "\\end{bmatrix}\n",
    "y = \\begin{bmatrix}\n",
    "{10}\\\\\n",
    "{28}\\\\\n",
    "\\end{bmatrix}\n",
    "\\Rightarrow\n",
    "\\begin{bmatrix}\n",
    "{x}\\\\\n",
    "{2x}\\\\\n",
    "\\end{bmatrix}\n",
    "+\\begin{bmatrix}\n",
    "{y}\\\\\n",
    "{4y}\\\\\n",
    "\\end{bmatrix}\n",
    " = \\begin{bmatrix}\n",
    "{10}\\\\\n",
    "{28}\\\\\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "由于要保证对应的分量相等，所以自然我们就可以恢复出方程$\\eqref{eq1}$.\n",
    "上面这个过程，向量的计算有两种：\n",
    "- 一个数乘一个向量；\n",
    "- 一个向量加一个向量；\n",
    "显然，当变量个数变多之后，也会满足上面这两种运算法则，因此我们接下来正式引入向量的基本运算法则：\n",
    "\n",
    "给定$n$维向量\n",
    "$$\n",
    "x= \\begin{bmatrix}\n",
    "{x_1}\\\\\n",
    "{x_2}\\\\\n",
    "{\\vdots}\\\\\n",
    "{x_n}\n",
    "\\end{bmatrix},\n",
    "y= \\begin{bmatrix}\n",
    "{y_1}\\\\\n",
    "{y_2}\\\\\n",
    "{\\vdots}\\\\\n",
    "{y_n}\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "- 向量的加法定义为：\n",
    "$$\n",
    "x+y = \\begin{bmatrix}\n",
    "{x_1 + y_1}\\\\\n",
    "{x_2 + y_2}\\\\\n",
    "{\\vdots}\\\\\n",
    "{x_n + y_n}\n",
    "\\end{bmatrix},\n",
    "$$\n",
    "即两个向量对应的分量相加.\n",
    "\n",
    "- 向量的数乘定义为：\n",
    "对于$k \\in \\mathbf{R}$,\n",
    "$$\n",
    "kx = \\begin{bmatrix}\n",
    "{kx_1 }\\\\\n",
    "{kx_2}\\\\\n",
    "{\\vdots}\\\\\n",
    "{kx_n}\n",
    "\\end{bmatrix},\n",
    "$$\n",
    "即每个分量都乘上$k$.\n",
    "\n",
    "关于向量与向量的乘法，在后续的学习中，我们再进一步介绍.我们约定一个使用习惯，我们默认所有的向量都采用列向量的形式，如上面所示.当我们在文中书写时，为了排版优美，通常将向量由列向量转成行向量进行书写，向量的行列交换的称为向量的**转置**，记做$x^T = (x_1, x_2, \\cdots, x_n)$.我们使用```Numpy```实现向量之间的基本计算."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "dd8c3934",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-05-27T13:36:01.359821Z",
     "start_time": "2022-05-27T13:36:01.339853Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x=[1 2 3],y=[4 5 6]\n",
      "x的维度为(3,)\n",
      "x+y = [5 7 9]\n",
      "kx = [3 6 9]\n",
      "3x+2y =[11 16 21] \n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "# 生成向量\n",
    "x = np.array([1, 2, 3]) # array默认如果只有一列，就是一个向量\n",
    "y = np.array([4, 5, 6])\n",
    "print(\"x={},y={}\".format(x, y))\n",
    "print(\"x的维度为{}\".format(x.shape)) # shape函数用于显示向量的维度，如果是向量默认只有一维，维度显示为(dim,)\n",
    "\n",
    "# 向量加法\n",
    "print(\"x+y = {}\".format(x + y))\n",
    "\n",
    "# 向量数乘\n",
    "k = 3\n",
    "print(\"kx = {}\".format(k*x))\n",
    "\n",
    "print(\"3x+2y ={} \".format(3*x + 2*y))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77095609",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-05-18T15:37:55.362301Z",
     "start_time": "2022-05-18T15:37:55.356317Z"
    }
   },
   "source": [
    "我们从几何角度来看这个事情，看看向量的加法与数乘在做什么：\n",
    "![](./figures/2-1.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c092f226",
   "metadata": {},
   "source": [
    "做好前面的铺垫后，现在我们可以把空间的概念引进来. 在二维空间中，更准确的说在几何空间中，空间存在无数个类似于$[x_1,y_1],[x_2,y_2]$的几何向量，同时空间中还存在控制几何向量之间的相互关系的运算：加法与数乘.举个不太恰当的例子：人类社会中，除了有存在空间中的人以外，还存在着约束每个人的道德与法律.那么n维空间也是一样的，里面存在着无数个n维向量$(x_1,x_2,...,x_n)^T,(y_1,y_2,...,y_n)^T$，同时存在约束着这些向量运算规则的加法和数乘.\n",
    "\n",
    "至此我们已经回答了第(2)个问题，高维的向量只要是有限维的都是满足我们上面加法与数乘的运算法则的.下面我们想来讨论，对于多个未知数的方程组，什么样的方程组才是有解的？\n",
    "\n",
    "### 2.2.2 向量的线性相关与线性无关"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d9ceb2fa",
   "metadata": {},
   "source": [
    "首先我们需要介绍几个研究向量的工具，我们先来看方程组$\\eqref{eq5}$为什么没有解，主要的原因是：从式子化简的结果来说，第一个式子跟第三个式子表达的是一个意思.看另外一个例子\n",
    "$$\n",
    "\\left\\{\\begin{array}{l}\n",
    "x + y + z = 14 \\\\\n",
    "2x+4y + 2z = 40 \\\\\n",
    "3x + 5y + 3z = 54\n",
    "\\end{array}\\right.\\label{eq10}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "15496a82",
   "metadata": {},
   "source": [
    "这个方程组，如果你尝试求解的话也会显示```Singular matrix```，仔细观察就会发现第三个式子是由，第一个式子和第二个式子相加得到的，所以第三个式子的信息已经包含在上面两个式子中了，那么我们如何才能一眼看出“式子是有效的”呢？我们拿出一件工具——**向量的线性相关与线性无关**.\n",
    "给定一组向量$(\\alpha_1, \\alpha_2, \\cdots, \\alpha_k)$（注意，这个地方之所以没有转置符号，是因为这是一个向量组，每个$\\alpha$都是一个列向量，需要与向量的写法做区分），对于向量$\\beta$，如果能被存在一组不全为0的常数$m_1, m_2, \\cdots, m_k$，使得\n",
    "$$\\beta = m_1\\alpha_1 + m_2\\alpha_2 + \\cdots + m_k\\alpha_k$$\n",
    "则称向量$\\beta$与向量组$(\\alpha_1, \\alpha_2, \\cdots, \\alpha_k)$是线性相关的，或称$\\beta$可以被向量组$(\\alpha_1, \\alpha_2, \\cdots, \\alpha_k)$线性表出.一旦向量是线性相关的，也就说明“$\\beta$是一个多余的向量，因为它可以由其他的向量去表示”.\n",
    "\n",
    "对于方程组$\\eqref{eq10}$,如果我们把第$i$个方程当成是一个向量$\\alpha_i$（这是不严谨的说法），则$\\alpha_3 = \\alpha_1 + \\alpha_2$，因此第三个方程是多余的.\n",
    "\n",
    "反之，如果$$m_0\\beta + m_1\\alpha_1 + m_2\\alpha_2 + \\cdots + m_k\\alpha_k = 0$$当且仅当$m_0, m_1, m_2, \\cdots, m_k$全都为0，则称$\\beta, \\alpha_1, \\alpha_2, \\cdots, \\alpha_k$是线性无关的."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a52a4bba",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-05-18T16:10:02.677008Z",
     "start_time": "2022-05-18T16:10:02.673016Z"
    }
   },
   "source": [
    "到目前为止，判断一个方程组有唯一解我们有两条法则：\n",
    "- $n$个未知数要有$n$个方程\n",
    "- 可以使用线性无关去判断“有效的方程”\n",
    "\n",
    "然而，如果当一个方程组未知数的量很大之后，你需要去判断哪些方程是“有效的”也是一件非常花时间的工作，有没有一个更好的方法呢，答案是有的，我们先介绍**行列式的概念**.在2.1.1中我们已经介绍了矩阵就是一种数表，而对于我们现在的问题而言，系数矩阵$A$总是行数、列数相等的，因为它的方程个数等于未知数的个数，像这样行数等于列数的矩阵我们称为**方阵**.对于方阵而言，我们可以计算它的行列式$|A|$，用```Numpy```实现如下："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "a6dd2b9b",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-05-27T13:36:27.183148Z",
     "start_time": "2022-05-27T13:36:27.160210Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A的行列式的值为： 0.0\n",
      "B的行列式的值为： -2.0\n"
     ]
    }
   ],
   "source": [
    "A = np.array([[1, 1, 1],\n",
    "              [2, 4, 2],\n",
    "              [2, 2, 2]])\n",
    "\n",
    "np.linalg.det(A) # 计算方阵A的行列式\n",
    "print(\"A的行列式的值为：\",np.linalg.det(A))\n",
    "\n",
    "B = np.array([[1,1,1,1],\n",
    "              [1,2,0,0],\n",
    "              [1,0,3,0],\n",
    "              [1,0,0,4]])\n",
    "B_det = np.linalg.det(B)\n",
    "print(\"B的行列式的值为：\",B_det)\n",
    "\n",
    "# B = np.array([[1,1,1,1],\n",
    "#               [1,2,0,0],\n",
    "#               [1,0,0,4]])# 你可以尝试用非方阵计算行列式，压根没法算！"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9c0122a",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger\" role=\"alert\">\n",
    "注意：一定要是方阵才能求行列式！\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f12a8a0",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-05-18T16:23:09.079332Z",
     "start_time": "2022-05-18T16:23:09.073121Z"
    }
   },
   "source": [
    "有了行列式之后，以后只要我们判断了一个方程组：\n",
    "1. 未知数个数等于方程的个数\n",
    "2. 系数行列式$|A| \\neq 0$\n",
    "则这个方程组是有唯一解的.\n",
    "\n",
    "上面这个判断的法则就是著名的**克莱姆法则(Cramer's Rule)**，更重要的是，克莱姆法则提出了一种解的结构：\n",
    "\n",
    "设线性方程组的表达式为：$\\left\\{\\begin{array}{c}a_{11} x_{1}+a_{12} x_{2}+\\cdots+a_{1 n} x_{n}=b_{1} \\\\ a_{21} x_{1}+a_{22} x_{2}+\\cdots+a_{2 n} x_{n}=b_{2} \\\\ \\cdots \\cdots \\\\ a_{n 1} x_{1}+a_{n 2} x_{2}+\\cdots+a_{n n} x_{n}=b_{n}\\end{array}\\right.$\n",
    "，系数行列式为：$D = \\left|\\begin{array}{cccc}a_{11} & a_{12} & \\cdots & a_{1 n} \\\\ a_{21} & a_{22} & \\cdots & a_{2 n} \\\\ \\cdots & \\cdots & \\cdots & \\cdots \\\\ a_{n 1} & a_{n 2} & \\cdots & a_{m n}\\end{array}\\right| \\neq 0$，则该线性方程组有且仅有唯一解:\n",
    "\n",
    "$$\n",
    "x_{1}=\\frac{D_{1}}{D}, x_{2}=\\frac{D_{2}}{D}, \\cdots, x_{n}=\\frac{D_{n}}{D}\n",
    "$$\n",
    "\n",
    "其中，$D_{j}=\\left|\\begin{array}{ccccccc}a_{11} & \\cdots & a_{1, j-1} & b_{1} & a_{1, j+1} & \\cdots & a_{1 n} \\\\ a_{21} & \\cdots & a_{2, j-1} & b_{2} & a_{2, j+1} & \\cdots & a_{2 n} \\\\ \\cdots & \\cdots & \\cdots & \\cdots & \\cdots & \\cdots & \\cdots \\\\ a_{n 1} & \\cdots & a_{n, j-1} & b_{n} & a_{n, j+1} & \\cdots & a_{n n}\\end{array}\\right|$\n",
    "\n",
    "<div class=\"alert alert-info\" role=\"alert\">\n",
    "🌰举个例子：\n",
    "解线性方程组 $\\left\\{\\begin{array}{l}2 x_{1}+x_{2}-5 x_{3}+x_{4}=8 \\\\ x_{1}-3 x_{2}-6 x_{4}=9 \\\\ 2 x_{2}-x_{3}+2 x_{4}=-5 \\\\ x_{1}+4 x_{2}-7 x_{3}+6 x_{4}=0\\end{array}\\right.$\n",
    "</div>\n",
    "\n",
    "**解：**方程组的系数行列式\n",
    "$$\n",
    "D=\\left|\\begin{array}{cccc}\n",
    "2 & 1 & -5 & 1 \\\\\n",
    "1 & -3 & 0 & -6 \\\\\n",
    "0 & 2 & -1 & 2 \\\\\n",
    "1 & 4 & -7 & 6\n",
    "\\end{array}\\right|=27 \\neq 0\n",
    "$$\n",
    "由克莱姆法则知：方程组有唯一解.\n",
    "\n",
    "$D_{1}=\\left|\\begin{array}{cccc}8 & 1 & -5 & 1 \\\\ 9 & -3 & 0 & -6 \\\\ -5 & 2 & -1 & 2 \\\\ 0 & 4 & -7 & 6\\end{array}\\right|=81 \\Rightarrow x_{1}=\\frac{D_{1}}{D}=\\frac{81}{27} = 3$，\n",
    "$D_{2}=\\left|\\begin{array}{cccc}2 & 8 & -5 & 1 \\\\ 1 & 9 & 0 & -6 \\\\ 0 & -5 & -1 & 2 \\\\ 1 & 0 & -7 & 6\\end{array}\\right|=-108 \\Rightarrow x_{2}=\\frac{D_{2}}{D} =\\frac{-108}{27}= 4$，$D_{3}=\\left|\\begin{array}{cccc}2 & 1 & 8 & 1 \\\\ 1 & -3 & 9 & -6 \\\\ 0 & 2 & -5 & 2 \\\\ 1 & 4 & 0 & 6\\end{array}\\right|=-27 \\Rightarrow x_{3}=\\frac{D_{3}}{D} = =\\frac{-27}{27}=-1$，$D_{4}=\\left|\\begin{array}{cccc}2 & 1 & -5 & 8 \\\\ 1 & -3 & 0 & 9 \\\\ 0 & 2 & -1 & -5 \\\\ 1 & 4 & -7 & 0\\end{array}\\right|=27 \\Rightarrow x_{4}=\\frac{D_{4}}{D} = \\frac{27}{27} = 1$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "92dcba29",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-05-27T13:36:34.437617Z",
     "start_time": "2022-05-27T13:36:34.413640Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "克拉默法则解线性方程组的解为：\n",
      " x1=3.00,\n",
      " x2=-4.00,\n",
      " x3=-1.00,\n",
      " x4=1.00\n"
     ]
    }
   ],
   "source": [
    "# 使用python实现克拉默法则：\n",
    "D = np.array([[2.,1,-5,1],[1,-3,0,-6],[0,2,-1,2],[1,4,-7,6]])\n",
    "D_det = np.linalg.det(D)\n",
    "\n",
    "D1 = np.array([[8.,1,-5,1],[9,-3,0,-6],[-5,2,-1,2],[0,4,-7,6]])\n",
    "D1_det = np.linalg.det(D1)\n",
    "\n",
    "D2 = np.array([[2.,8,-5,1],[1,9,0,-6],[0,-5,-1,2],[1,0,-7,6]])\n",
    "D2_det = np.linalg.det(D2)\n",
    "\n",
    "D3 = np.array([[2.,1,8,1],[1,-3,9,-6],[0,2,-5,2],[1,4,0,6]])\n",
    "D3_det = np.linalg.det(D3)\n",
    "\n",
    "D4 = np.array([[2.,1,-5,8],[1,-3,0,9],[0,2,-1,-5],[1,4,-7,0]])\n",
    "D4_det = np.linalg.det(D4)\n",
    "\n",
    "x1 = D1_det / D_det\n",
    "x2 = D2_det / D_det\n",
    "x3 = D3_det / D_det\n",
    "x4 = D4_det / D_det\n",
    "print(\"克拉默法则解线性方程组的解为：\\n x1={:.2f},\\n x2={:.2f},\\n x3={:.2f},\\n x4={:.2f}\".format(x1,x2,x3,x4))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d7c47716",
   "metadata": {},
   "source": [
    "事实上从用的角度上说，这事到这里就结束了，但是你会发现我们还没说行列式是什么:)\n",
    "\n",
    "下面我们详细介绍行列式的概念.[如果你看到数学就头晕目眩，可以直接跳到2.2.3]\n",
    "\n",
    "先看一个式子: $D_{2}=\\left|\\begin{array}{ll}a_{11} & a_{12} \\\\ a_{21} & a_{22}\\end{array}\\right|$. 我们称其为 2 阶行列式,其中 $a_{i j}$ 的第一个下标 $i$ 表示此元素所在的行数,第二个下标 $j$ 表示此元素所在的列数, $i=1,2, j=1,2$,于是此行列式中有四个元素,并且 $\\left|\\begin{array}{ll}a_{11} & a_{12} \\\\ a_{21} & a_{22}\\end{array}\\right|=$ $a_{11} a_{22}-a_{12} a_{21} .$ 这是一个什么样的计算规则 $?$ 它背后有什么样的意义?\n",
    "\n",
    "将此行列式的第 1 行的两个元素 $a_{11}, a_{12}$ 看成一个 2 维向量$\\left[a_{11}, a_{12}\\right]{:=} \\boldsymbol{\\alpha}_{1}$，第二行的两个元素 $a_{21}, a_{22}$ 看成另一个 2 维向量 $\\left[a_{21}, a_{22}\\right]{:=} \\boldsymbol{\\alpha}_{2}$.不妨设 $\\boldsymbol{\\alpha}_{1}$ 的长度(模)为 $l, \\boldsymbol{\\alpha}_{2}$ 的长度(模)为 $m, \\boldsymbol{\\alpha}_{1}$ 与 $x$ 轴正向的夹角为 $\\alpha, \\boldsymbol{\\alpha}_{2}$ 与 $x$ 轴正向的夹角为 $\\beta$, 于是,如图所示：\n",
    "\n",
    "![jupyter](./figures/2-2.png)\n",
    "\n",
    "则：\n",
    "$$\n",
    "\\begin{aligned}\n",
    "S_{\\square O A B C} &=l \\cdot m \\cdot \\sin (\\beta-\\alpha) \\\\\n",
    "&=l \\cdot m(\\sin \\beta \\cos \\alpha-\\cos \\beta \\sin \\alpha) \\\\\n",
    "&=l \\cos \\alpha \\cdot m \\sin \\beta-l \\sin \\alpha \\cdot m \\cos \\beta \\\\\n",
    "&=a_{11} a_{22}-a_{12} a_{21}\n",
    "\\end{aligned}\n",
    "$$\n",
    "因此：\n",
    "$$\n",
    "\\left|\\begin{array}{ll}\n",
    "a_{11} & a_{12} \\\\\n",
    "a_{21} & a_{22}\n",
    "\\end{array}\\right|=a_{11} a_{22}-a_{12} a_{21}=S_{\\square O A B C}\n",
    "$$\n",
    "我们看到了一个极其直观有趣的结论: 2 阶行列式是由两个 2 维向量组成的,其(运算规则的)结果为 以这两个向量为邻边的平行四边形的面积. 这不仅得出了 2 阶行列式的计算规则，也能够清楚地看到其几何意义.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c2c2074",
   "metadata": {},
   "source": [
    "### 2.2.3 矩阵"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2b508aaf",
   "metadata": {},
   "source": [
    "回想一下中学阶段在解方程组的场景：每次将方程组抄一遍，消掉一个未知数，又抄一遍，又消掉一个未知数，又抄一遍······这个过程一直持续，非常麻烦，直到最后一个方程可以被解出来，我们希望有一些更简便的记录方法，下面我们介绍另一个非常强大的工具——**矩阵**，但大家学习矩阵前一定要在心里默念十遍：矩阵不仅仅只是用来解方程！它又非常强大的功能，在后面的章节中，我们将一步一步介绍，在这里我们先介绍一些矩阵的基本运算以及在解方程中的应用."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4cbfacf0",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-05-27T13:16:30.312889Z",
     "start_time": "2022-05-27T13:16:30.302915Z"
    }
   },
   "source": [
    "在之前学过的高斯消元法中，我们对方程有些等价变换，对方程组做了这些变换后，对方程的解是不改变的：\n",
    "$$\n",
    "\\left\\{\\begin{array}{l}\n",
    "x + y + z = 14 \\\\\n",
    "2x+4y + 2z = 40 \n",
    "\\end{array}\\right.\n",
    "\\stackrel{交换两个方程的位置}{\\longrightarrow}\n",
    "\\left\\{\\begin{array}{l}\n",
    "2x+4y + 2z = 40 \\\\\n",
    "x + y + z = 14\n",
    "\\end{array}\\right.\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\left\\{\\begin{array}{l}\n",
    "x + y + z = 14 \\\\\n",
    "2x+4y + 2z = 40 \n",
    "\\end{array}\\right.\n",
    "\\stackrel{等号两边同乘一个非零常数}{\\longrightarrow}\n",
    "\\left\\{\\begin{array}{l}\n",
    "2x + 2y + 2z = 28 \\\\\n",
    "2x+4y + 2z = 40 \n",
    "\\end{array}\\right.\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\left\\{\\begin{array}{l}\n",
    "x + y + z = 14 \\\\\n",
    "2x+4y + 2z = 40 \n",
    "\\end{array}\\right.\n",
    "\\stackrel{一个方程加到另外一个方程上导出一个新方程}{\\longrightarrow}\n",
    "\\left\\{\\begin{array}{l}\n",
    "x + y + z = 14 \\\\\n",
    "2x+4y + 2z = 40 \\\\\n",
    "3x + 5y + 3z = 54\n",
    "\\end{array}\\right.\n",
    "$$\n",
    "\n",
    "\n",
    "如上，**交换两个方程的位置**、**一个方程等号两边同乘一个非零常数$k$**，**一个方程加到另外一个方程上导出一个新方程**，这三种操作显然不会改变方程组的解. 那么我们让计算机知道要做这些操作呢，矩阵建立起了这其中的关系. \n",
    "\n",
    "对于一个矩阵$A$，假设行数为$n$，列数为$m$，则它的维度为$n \\times m$，记作：$A_{n\\times m}$. 当两个矩阵要做**乘法**时，我们要求前一个矩阵的列数要等于后一个矩阵的行数，即：给定$A_{a\\times b},B_{c \\times d}$，若$AB$有意义，则$b=c$，并且结果的维度为$a\\times d$，结果矩阵的第$ij$个元素为：**前一个矩阵的第$i$个行向量与后一个矩阵第$j$个列点乘得到**. 也正是如此，我们不能对矩阵乘法轻易交换顺序，也就是说$AB$不一定等于$BA$，这个一定要注意！\n",
    "我们只需要记住这些前提，剩下的事情交给计算机."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "b4bd681d",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-05-27T13:52:21.580432Z",
     "start_time": "2022-05-27T13:52:21.565452Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A的规模(2, 2)\n",
      "B的规模(2, 3)\n",
      "AB=\n",
      "[[-1  4  1]\n",
      " [ 2  1 -5]]\n"
     ]
    }
   ],
   "source": [
    "A = np.array([[1, 2],\n",
    "              [1, -1]])\n",
    "B = np.array([[1, 2, -3],\n",
    "              [-1, 1, 2]])\n",
    "\n",
    "print(\"A的规模{}\".format(A.shape))\n",
    "print(\"B的规模{}\".format(B.shape))\n",
    "\n",
    "# 计算AB\n",
    "print(\"AB=\\n{}\".format(np.matmul(A, B)))\n",
    "\n",
    "# 计算BA会报错维度不对应\n",
    "# np.matmul(B, A)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "faa785f2",
   "metadata": {},
   "source": [
    "此外，两个维度大小一个矩阵可以做加法，即对应位置元素相加. 一个矩阵乘一个常数等于每个位置的元素都乘这个常数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "d80694e5",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-05-27T13:57:34.358658Z",
     "start_time": "2022-05-27T13:57:34.343655Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A+C = \n",
      " [[2 4]\n",
      " [4 3]]\n",
      "3*A = \n",
      " [[ 3  6]\n",
      " [ 3 -3]]\n"
     ]
    }
   ],
   "source": [
    "A = np.array([[1, 2],\n",
    "              [1, -1]])\n",
    "C = np.array([[1, 2],\n",
    "                [3, 4]])\n",
    "print(\"A+C = \\n\", A + C) # A+C \n",
    "print(\"3*A = \\n\", 3 * A) # 3*A\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cc0a9b9b",
   "metadata": {},
   "source": [
    "下面我们介绍一些特殊的矩阵，这些矩阵对应着一些特殊变换.\n",
    "#### 1. **单位矩阵**\n",
    "在矩阵的乘法中，有一种矩阵起着特殊的作用，如同数的乘法中的1，这种矩阵被称为单位矩阵. 它是个方阵，从左上角到右下角的对角线（称为主对角线）上的元素均为1，除此以外全都为0.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "bf8ebede",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-05-27T14:08:29.250380Z",
     "start_time": "2022-05-27T14:08:28.795076Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B =\n",
      " [[ 1  2 -3]\n",
      " [-1  1  2]] \n",
      " E = \n",
      " [[1. 0. 0.]\n",
      " [0. 1. 0.]\n",
      " [0. 0. 1.]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  2., -3.],\n",
       "       [-1.,  1.,  2.]])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(\"B =\\n\", B,\"\\n\", \"E = \\n\", np.eye(3)) # 3阶单位阵\n",
    "\n",
    "np.matmul(B, np.eye(3))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0c5b8895",
   "metadata": {},
   "source": [
    "#### 2.初等矩阵\n",
    "如果你想让计算机懂得解方程组的三个步骤，首先我们先抽象出一个方程组的系数矩阵$A_{n\\times m} $，假设下面介绍三个操作对应的矩阵变换，称为初等矩阵：\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "ccb5d606",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-05-27T14:24:40.203178Z",
     "start_time": "2022-05-27T14:24:40.186224Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A = \n",
      " [[1 1 1]\n",
      " [2 4 2]]\n"
     ]
    }
   ],
   "source": [
    "A = np.array([[1, 1, 1],\n",
    "              [2, 4, 2]])\n",
    "print(\"A = \\n\", A)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0f154cb7",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-05-27T14:23:50.425773Z",
     "start_time": "2022-05-27T14:23:50.405826Z"
    }
   },
   "source": [
    "1. **交换第$i$个与第$j$个方程↔️系数矩阵第$i$行与第$j$行互换↔️左乘一个($P_{n \\times n}$)，$P$为单位阵$E_{n}$第$i$行与第$j$行互换**\n",
    "$$\n",
    "\\left\\{\\begin{array}{l}\n",
    "x + y + z = 14 \\\\\n",
    "2x+4y + 2z = 40 \n",
    "\\end{array}\\right.\n",
    "\\Rightarrow\n",
    "\\left\\{\\begin{array}{l}\n",
    "2x+4y + 2z = 40 \\\\\n",
    "x + y + z = 14\n",
    "\\end{array}\\right.\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "80ae168a",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-05-27T14:28:06.183156Z",
     "start_time": "2022-05-27T14:28:06.163209Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2, 4, 2],\n",
       "       [1, 1, 1]])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P = np.array([[0, 1],\n",
    "              [1, 0]])\n",
    "np.matmul(P, A) # 交换了矩阵的两行"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5f6c51ae",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-05-27T14:33:51.548919Z",
     "start_time": "2022-05-27T14:33:51.528974Z"
    }
   },
   "source": [
    "2. **第$i$个方程左右乘非零常数$k$倍↔️系数矩阵第$i$行乘$k$↔️左乘一个($P_{n \\times n}$)，$P$为单位阵$E_{n}$第$i$行乘$k$**\n",
    "$$\n",
    "\\left\\{\\begin{array}{l}\n",
    "x + y + z = 14 \\\\\n",
    "2x+4y + 2z = 40 \n",
    "\\end{array}\\right.\n",
    "\\Rightarrow\n",
    "\\left\\{\\begin{array}{l}\n",
    "2x + 2y + 2z = 28 \\\\\n",
    "2x+4y + 2z = 40 \n",
    "\\end{array}\\right.\n",
    "$$\n",
    "[注] 本来应该增广矩阵乘$k$倍，但我们这里仅讨论了系数矩阵，这种做法不太严谨！"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "cd0953ff",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-05-27T14:36:20.232507Z",
     "start_time": "2022-05-27T14:36:20.214520Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2, 2, 2],\n",
       "       [2, 4, 2]])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P = np.array([[2, 0],\n",
    "              [0, 1]])\n",
    "np.matmul(P, A) # 第$i$行乘$k$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a29dd00f",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-05-27T14:58:02.263190Z",
     "start_time": "2022-05-27T14:58:02.243242Z"
    }
   },
   "source": [
    "3. **第$i$个方程加到第$j$个方程中↔️系数矩阵第$i$行加到第$j$行↔️左乘一个($P_{n \\times n}$)，$P$为单位阵$E_{n}$第$i$行加到第$j$行**\n",
    "$$\n",
    "\\left\\{\\begin{array}{l}\n",
    "x + y + z = 14 \\\\\n",
    "2x+4y + 2z = 40 \n",
    "\\end{array}\\right.\n",
    "\\Rightarrow\n",
    "\\left\\{\\begin{array}{l}\n",
    "2x + 2y + 2z = 28 \\\\\n",
    "3x+5y + 3z = 44 \n",
    "\\end{array}\\right.\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "a59b5b35",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-05-27T14:58:28.231454Z",
     "start_time": "2022-05-27T14:58:28.220483Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 1, 1],\n",
       "       [3, 5, 3]])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P = np.array([[1, 0],\n",
    "              [1, 1]])\n",
    "np.matmul(P, A) # 第$i$行乘$k$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "320b9ca8",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-05-27T15:00:08.142234Z",
     "start_time": "2022-05-27T15:00:08.125279Z"
    }
   },
   "source": [
    "有了这三类矩阵之后，你可以构建一个矩阵$P = P_1P_2\\cdots C_k$，即等于一列初等矩阵的乘积，那么就可以实现对方程组的系数进行操作，例如对方程组交换两行后，将原来第一行（交换后的第二行）乘两倍，最后加到第二行上.\n",
    "\n",
    "我们先分开做一下："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "bf276047",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-05-27T15:06:39.367141Z",
     "start_time": "2022-05-27T15:06:39.338242Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4, 8, 4],\n",
       "       [5, 9, 5]])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.array([[1, 1, 1],\n",
    "              [2, 4, 2]])\n",
    "# 方程组交换两行\n",
    "P1 = np.array([[0, 1],\n",
    "              [1, 0]])\n",
    "A = np.matmul(P1, A)\n",
    "\n",
    "# 原来第一行（交换后的第二行）乘两倍\n",
    "P2 = np.array([[0, 1],\n",
    "              [2, 0]])\n",
    "A = np.matmul(P2, A)\n",
    "\n",
    "# 第一行加到第二行上\n",
    "P3 = np.array([[0, 1],\n",
    "              [1, 1]])\n",
    "A = np.matmul(P3, A)\n",
    "\n",
    "A"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1981a3c1",
   "metadata": {},
   "source": [
    "计算矩阵$P$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "efc21622",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-05-27T15:10:21.265205Z",
     "start_time": "2022-05-27T15:10:21.245100Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P = \n",
      " [[0 2]\n",
      " [1 0]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[4, 8, 4],\n",
       "       [1, 1, 1]])"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.array([[1, 1, 1],\n",
    "              [2, 4, 2]])\n",
    "\n",
    "P = np.matmul(P1, P2)\n",
    "P = np.matmul(P, P1)\n",
    "print(\"P = \\n\", P)\n",
    "\n",
    "np.matmul(P, A)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f9fefb82",
   "metadata": {},
   "source": [
    "这里必须说一下，由于在方程中我们一般只做行变换，所以对应的是变换矩阵$P$在左边乘系数矩阵，称为：**左乘**. 在其他场景里，我们可以对矩阵进行列变换，那么相应的是**右乘**一个变换矩阵$P$.\n",
    "\n",
    "❗这里我们再次强调了为什么矩阵的乘法是一般是不能交换的，因为对应的含义完全不同！"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "553e2e78",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-05-27T15:16:05.767022Z",
     "start_time": "2022-05-27T15:16:05.746934Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "交换两行：\n",
      " [[3 4]\n",
      " [1 2]]\n",
      "交换两列：\n",
      " [[2 1]\n",
      " [4 3]]\n"
     ]
    }
   ],
   "source": [
    "A = np.array([[1, 2],\n",
    "              [3, 4]])\n",
    "P = np.array([[0, 1],\n",
    "              [1, 0]])\n",
    "\n",
    "print(\"交换两行：\\n\", np.matmul(P, A))\n",
    "print(\"交换两列：\\n\", np.matmul(A, P))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "18cee272",
   "metadata": {},
   "source": [
    "这下我们知道了，矩阵就类似一种功能模块，我要对行执行这种功能，就左乘一种“功能”，要对列执行这种功能，就右乘“功能”."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4201aa10",
   "metadata": {},
   "source": [
    "事实上，对于任意一个线性方程组，我们都可以抽象成这样的形式\n",
    "$$Ax=b,$$\n",
    "其中，矩阵$A$是系数矩阵，$x$是由未知数构成的向量，$b$是常数向量.为了解这样的方程，凭借小学二年级的知识，我们很希望可以将$A$“除过去”变成$\\frac{b}{A}$，事实上这个写法是不对的，只是为了大家理解，在矩阵中我们没有定义除法，为了实现类似的功能，我们定义矩阵的逆.\n",
    "\n",
    "对于$n$阶方阵$A$，如果存在一个$n$阶方阵$B$，使得\n",
    "$$AB=BA=E_n$$\n",
    "则我们称$A$是可逆的，$B$是$A$的逆矩阵，记做$A^{-1}$.\n",
    "\n",
    "如果一个矩阵是可逆的，那么首先它一定要是个方阵，也就是行数等于列数，此外它还要满足行列式不等于0，也就是我们上面提到的**非奇异矩阵**.我们在此不给出严格的证明，这个可以联想除法去理解，当你要“除”过去，作为“分母”自然不能为0.\n",
    "\n",
    "至于如何计算，我们可以通过```Numpy```模块求解："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "0b8acff5",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-06-01T03:06:29.209066Z",
     "start_time": "2022-06-01T03:06:29.189120Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-2.0000000000000004 行列式不为0，非奇异阵\n",
      "A的逆矩阵：\n",
      " [[-2.   1. ]\n",
      " [ 1.5 -0.5]]\n",
      "验证AA_inv = E \n",
      " [[1.00000000e+00 1.11022302e-16]\n",
      " [0.00000000e+00 1.00000000e+00]]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "A = np.array([[1, 2], [3, 4]])\n",
    "print(np.linalg.det(A),\"行列式不为0，非奇异阵\") # 检验是否奇异\n",
    "print(\"A的逆矩阵：\\n\", np.linalg.inv(A)) # 矩阵求逆\n",
    "\n",
    "A_inv = np.linalg.inv(A)\n",
    "\n",
    "print(\"验证AA_inv = E \\n\", np.matmul(A, A_inv))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "955705b8",
   "metadata": {},
   "source": [
    "这里看着不像单位阵，但实际上是因为数值计算带来的后果，我们仅需要做一下数值过滤即可.事实上，为了一些应用更加简便，对于非奇异阵我们也定义了\"伪逆\".\n",
    "它的定义是这样的：对于任意一个矩阵$A \\in \\mathbb{R}^{n\\times m}$，存在一个矩阵$A^g \\in \\mathbb{R}^{m\\times n}$，使得$AA^gA=A$，则称$A^g$为$A$的**伪逆**(广义逆).\n",
    "\n",
    "具体实现如下："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "afc9ffab",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-06-01T03:15:23.411257Z",
     "start_time": "2022-06-01T03:15:23.396239Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0 行列式为0，奇异阵\n",
      "[[ 0.   0. ]\n",
      " [ 0.5 -0.5]]\n",
      "[[ 0.  1.]\n",
      " [ 0. -1.]]\n"
     ]
    }
   ],
   "source": [
    "B = np.array([[0, 1],\n",
    "              [0, -1]])\n",
    "print(np.linalg.det(B),\"行列式为0，奇异阵\") # 检验是否奇异\n",
    "# print(\"B的逆矩阵：\\n\", np.linalg.inv(B)) # 直接求逆会报错\n",
    "\n",
    "print(np.linalg.pinv(B))\n",
    "print(np.matmul(np.matmul(B, np.linalg.pinv(B)),B)) # 验证广义逆的定义"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca03e963",
   "metadata": {},
   "source": [
    "接下来我们来研究矩阵的功能，矩阵是如何发挥出它的功能的呢？事实上，矩阵作用的基本元素是向量，我们可以把矩阵$A$看成一个由$m$个$n$维向量组成的方块. 那么要研究矩阵的功能，最首要的是看它在每个向量上的作用. 对于向量而言，最基本的不外乎是平移跟拉伸.\n",
    "\n",
    "我们提及一个重要的核心概念：**向量在空间中的位置是绝对的，而其坐标值却是相对的，坐标的取值依托于其所选取的坐标向量（基底).** 更直白的说就是，对于同一个向量，选取的坐标向量（基底）不同，其所对应的坐标值就不同.(下图来源于石溪)\n",
    "\n",
    "![jupyter](./figures/2-3.jpeg)\n",
    "\n",
    "从中我们可以看到：向量$a$在直角坐标系下与在基底$e_1^{'},e_2^{'}$下的坐标显然是不同.\n",
    "\n",
    "假设一个向量在坐标系$\\mathbb{1}$下表示的坐标为$x$，当这个向量$x$经过一个线性变换形成一个新的向量$y$，用矩阵表示这个变换就是：$y = Ax$，矩阵$A$对应着$x \\rightarrow y$的线性变换. 同时，向量也可以在坐标系$\\mathbb{2}$下表示，其坐标为$x^{'}$，那么$x^{'} = Px$. 同理，$x^{'}$也可以经过同一个线性变换变成$y^{'}$，即：$y^{'} = Bx^{'}=BPx$. 最后我们把$y^{'}$转化为同一个坐标系下表达，即$y=P^{-1}y^{'}=P^{-1}BPx$. 因此，我们可以得到：$Ax = P^{-1}BPx$，即：\n",
    "$$\n",
    "A = P^{-1}BP\n",
    "$$\n",
    "我们称满足上式的矩阵A、B称为相似矩阵. 总结一下：一个向量在空间位置里，选取不同的坐标系，其坐标值是不同的. 对于空间中同一个线性变换，在不同的坐标系下，用于描述这个变换的矩阵也是不同的, 而这些不同矩阵所描述的线性变换是相似的，因此我们称他们为**相似矩阵**.\n",
    "\n",
    "那知道相似矩阵的概念有什么用呢？一个矩阵代表着一个线性变换，而不同的坐标系又会得到不同的相似矩阵，那我们能不能选用一个最佳的坐标系，使得我们描述的这个线性变换的矩阵是最佳的呢？什么矩阵才能称得上是最佳矩阵呢？答案就是**对角矩阵**！因为当我们同时需要经历很多次线性变换的时候，对角矩阵能极大的减少我们的计算量，即：\n",
    "$$\n",
    "A^{n}=\\left[\\begin{array}{lll}\n",
    "a_{1} & & \\\\\n",
    "& a_{2} & \\\\\n",
    "& & a_{3}\n",
    "\\end{array}\\right]^{n}=\\left[\\begin{array}{lll}\n",
    "a_{1}^{n} & & \\\\\n",
    "& a_{2}^{n} & \\\\\n",
    "& & a_{3}^{n}\n",
    "\\end{array}\\right]\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "0ec2f8ab",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-05-27T15:59:40.543058Z",
     "start_time": "2022-05-27T15:59:40.522115Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 0, 0],\n",
       "       [0, 4, 0],\n",
       "       [0, 0, 9]])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.array([[1, 0, 0],\n",
    "              [0, 2, 0], \n",
    "              [0, 0, 3]])\n",
    "np.matmul(A, A)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bb882d57",
   "metadata": {},
   "source": [
    "那给你一组基，我们怎么将这组基转化成最优的基，即**对角矩阵**对应的基呢？【需要注意的是，并不是所有的矩阵都能相似于对角矩阵】\n",
    "\n",
    "首席按，我们的目标是：找到一个对角矩阵\n",
    "$\\Lambda=\\left[\\begin{array}{llll}\n",
    "\\lambda_{1} & & & \\\\\n",
    "& \\lambda_{2} & & \\\\\n",
    "& & \\cdots & \\\\\n",
    "& & & \\lambda_{n}\n",
    "\\end{array}\\right]$，使得\n",
    "$$P^{-1}AP = \\Lambda$$\n",
    "其中，矩阵 $P$ 和 $A$ 一样，均为 $n$ 阶方阵。\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "95cf12cf",
   "metadata": {},
   "source": [
    "我们直接给出结论，我们找到的对角矩阵的这些元素$\\lambda_i$,称为矩阵$A$的特征值，特征值会满足如下的定义：\n",
    "$$Ax = \\lambda_i x$$\n",
    "其中，$x$是一个非零向量，称为$A$的特征值$\\lambda_i$对应的特征向量.\n",
    "\n",
    "Python 已经帮我们集成好计算的工具了，下面我们给出代码："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "8dbd1c2a",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-05-27T16:39:36.547033Z",
     "start_time": "2022-05-27T16:39:36.528060Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "矩阵A的特征值为： [-1.  2.  2.]\n",
      "矩阵A的特征向量为：\n",
      " [[-0.70710678 -0.24253563  0.30151134]\n",
      " [ 0.          0.          0.90453403]\n",
      " [-0.70710678 -0.9701425   0.30151134]]\n",
      "矩阵A对角化为：\n",
      " [[-1.00000000e+00 -1.32062993e-16 -3.03478581e-16]\n",
      " [-1.60646788e-17  2.00000000e+00 -1.53475516e-17]\n",
      " [ 0.00000000e+00  0.00000000e+00  2.00000000e+00]]\n"
     ]
    }
   ],
   "source": [
    "# 使用python求解矩阵的特征值和特征向量\n",
    "A = np.array([[-2,1,1],\n",
    "             [0,2,0],\n",
    "             [-4,1,3]])\n",
    "lamb,p = np.linalg.eig(A)\n",
    "print(\"矩阵A的特征值为：\",lamb)\n",
    "print(\"矩阵A的特征向量为：\\n\",p)\n",
    "print(\"矩阵A对角化为：\\n\",np.matmul(np.linalg.inv(p),np.matmul(A,p)))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "80da9f8b",
   "metadata": {},
   "source": [
    "需要注意一件事，如果我们采用```Numpy```计算，本质上是一种数值计算，计算的结果是接近真实值的一种数值逼近结果，所以你会发现```-1.32062993e-16```这些非常小的数值，你可以将其作为0看待，那么就可以得到相应的对角化矩阵了. 即：\n",
    "$\\Lambda=\\left[\\begin{array}{lll}\n",
    "-1 & &  \\\\\n",
    "& 2 & & \\\\\n",
    "& & 2 \\end{array}\\right]$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "8c0ea789",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-05-27T16:39:39.455177Z",
     "start_time": "2022-05-27T16:39:39.434236Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-1.  0.  0.]\n",
      " [ 0.  2.  0.]\n",
      " [ 0.  0.  2.]]\n"
     ]
    }
   ],
   "source": [
    "# 数值过滤\n",
    "res = np.matmul(np.linalg.inv(p),np.matmul(A,p))\n",
    "res[np.abs(res) <1e-6] = 0 # 将绝对值小于10的-6次方的值设为0\n",
    "print(res)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e5a8e49e",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-05-27T16:20:06.373732Z",
     "start_time": "2022-05-27T16:20:06.328804Z"
    }
   },
   "source": [
    "下面我们来讲其中的数学原理，看到数学就头晕目眩的同学可以跳过！\n",
    "\n",
    "为了方便分析和描述，我们把矩阵$P$写成一组列向量并排 排列的形式： $P=\\left[\\begin{array}{llll}p_{1} & p_{2} & \\ldots & p_{n}\\end{array}\\right]$, 即 $n$ 个 $n$ 维列向量的横向排列。根据$P^{-1}AP = \\Lambda$，我们左乘一个矩阵$P$，得到：$A P=P \\Lambda$，具体展开：\n",
    "$$\n",
    "A\\left[p_{1}, p_{2}, \\ldots, p_{n}\\right]=\\left[p_{1}, p_{2}, \\ldots, p_{n}\\right]\\left[\\begin{array}{llll}\n",
    "\\lambda_{1} & & & \\\\\n",
    "& \\lambda_{2} & & \\\\\n",
    "& & \\cdots & \\\\\n",
    "& & & \\lambda_{n}\n",
    "\\end{array}\\right]\n",
    "$$\n",
    "进而可以得到：$\\left[A p_{1}, A p_{2}, \\ldots, A p_{n}\\right]=\\left[\\lambda_{1} p_{1}, \\lambda_{2} p_{2}, \\ldots, \\lambda_{n} p_{n}\\right]$。那么问题的答案就出来了：为了上面这个等式能成立, 就必须让左右两边的向量在每个维度上分别相等。即, $A p_{1}=\\lambda_{1} p_{1}, \\quad A p_{2}=\\lambda_{2} p_{2}, \\ldots, \\quad A p_{n}=\\lambda_{n} p_{n}$ 。\n",
    "\n",
    "总结一下：\n",
    "\n",
    "第一步是：我们要找到满足上述等式$A p_{1}=\\lambda_{1} p_{1}, \\quad A p_{2}=\\lambda_{2} p_{2}, \\ldots, \\quad A p_{n}=\\lambda_{n} p_{n}$的这一组向量 $p_{1}, p_{2}, \\ldots, p_{n}$ 。找到他们之后，我们将其横向排列，就构成了我们苦心寻找的转换矩阵 $P=\\left[\\begin{array}{llll}p_{1} & p_{2} & \\ldots & p_{n}\\end{array}\\right]$;\n",
    "\n",
    "第二步是：将分别与向量 $p_{1}, p_{2}, \\ldots, p_{n}$ 对应的值 $\\lambda_{1}, \\lambda_{2}, \\ldots \\lambda_{n}$ 依序沿着对角线排列，就构成 了与矩阵 $A$ 相似的对角矩阵 $\\Lambda=\\left[\\begin{array}{cccc}\\lambda_{1} & & & \\\\ & \\lambda_{2} & & \\\\ & & . & \\\\ & & & \\lambda_{n}\\end{array}\\right]$ 。\n",
    "\n",
    "那么对角化的问题就直接转化为了：如何找到满足等式$A p_{1}=\\lambda_{1} p_{1}, \\quad A p_{2}=\\lambda_{2} p_{2}, \\ldots, \\quad A p_{n}=\\lambda_{n} p_{n}$的一组向量$p_{1}, p_{2}, \\ldots, p_{n}$和对应的值$\\lambda_1,\\lambda_2,...,\\lambda_n$。首先，我们的等式为：$Ap = \\lambda p$，那么$Ap = \\lambda Ip$，$I$为单位矩阵。我们稍作变形：$(A-\\lambda I)p = 0$，那么如果这个$p$是有解的话，那么$A-\\lambda I$的行列式$det(A-\\lambda I)=0$。因此我们只需要解这个方程$det(A-\\lambda I)=0$就可以求出$\\lambda$和向量$p$了。\n",
    "\n",
    "重点来了：我们把满足$Ap = \\lambda p$的数值$\\lambda$为矩阵$A$的特征值，称$p$为矩阵$A$关于特征值$\\lambda$的特征向量。那特征值和特征向量有什么意义呢？不难看出，由于$Ap = \\lambda p$，而一个矩阵对应一个线性变换，因此经过矩阵A变换后的向量竟然是原向量的伸缩，因此特征向量就是那些经过矩阵A变换后的向量方向与变换前的方向相同或者相反的向量。\n",
    "\n",
    "最后给一个例子给大家演示下怎么求特征值和特征向量吧！\n",
    "\n",
    "<div class=\"alert alert-info\" role=\"alert\">\n",
    "🌰举个例子：\n",
    "求矩阵 $\\boldsymbol{A}=\\left(\\begin{array}{ccc}-1 & 1 & 0 \\\\ -4 & 3 & 0 \\\\ 1 & 0 & 2\\end{array}\\right)$ 的特征值和特征向量.[采用两种方式计算python与手算]\n",
    "</div>\n",
    "\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "|A-\\lambda E| &=\\left|\\begin{array}{ccc}\n",
    "-1-\\lambda & 1 & 0 \\\\\n",
    "-4 & 3-\\lambda & 0 \\\\\n",
    "1 & 0 & 2-\\lambda\n",
    "\\end{array}\\right|=(2-\\lambda)\\left|\\begin{array}{cc}\n",
    "-1-\\lambda & 1 \\\\\n",
    "-4 & 3-\\lambda\n",
    "\\end{array}\\right| \\\\\n",
    "&=(2-\\lambda)(\\lambda-1)^{2}=0\n",
    "\\end{aligned}\n",
    "$$\n",
    "特征值为 $\\lambda=\\mathbf{2}, \\mathbf{1}, \\mathbf{1}$。\n",
    "\n",
    "把每个特征值 $\\boldsymbol{\\lambda}$ 代入线性方程组 $(A-\\lambda E) x=0$， 求出基础解系。当 $\\lambda=2$ 时, 解线性方程组 $(A-2 E) x=0$。\n",
    "$$\n",
    "(A-2 E)=\\left(\\begin{array}{lll}\n",
    "-3 & 1 & 0 \\\\\n",
    "-4 & 1 & 0 \\\\\n",
    "1 & 0 & 0\n",
    "\\end{array}\\right) \\rightarrow\\left(\\begin{array}{lll}\n",
    "1 & 0 & 0 \\\\\n",
    "0 & 1 & 0 \\\\\n",
    "0 & 0 & 0\n",
    "\\end{array}\\right)\n",
    "$$\n",
    "$\\left\\{\\begin{array}{l}x_{1}=0 \\\\ x_{2}=0\\end{array} \\quad\\right.$ 得基础解系: $p_{1}=\\left(\\begin{array}{l}0 \\\\ 0 \\\\ 1\\end{array}\\right)$\n",
    "\n",
    "[后续过程略]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "454f9988",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-05-27T16:23:47.002896Z",
     "start_time": "2022-05-27T16:23:46.984916Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "矩阵A的特征值为： [2. 1. 1.]\n",
      "矩阵A的特征向量为：\n",
      " [[ 0.          0.40824829  0.40824829]\n",
      " [ 0.          0.81649658  0.81649658]\n",
      " [ 1.         -0.40824829 -0.40824829]]\n"
     ]
    }
   ],
   "source": [
    "# 使用python求解矩阵的特征值和特征向量\n",
    "A = np.array([[-1,1,0],\n",
    "             [-4,3,0],\n",
    "             [1,0,2]])\n",
    "lamb,p = np.linalg.eig(A)\n",
    "print(\"矩阵A的特征值为：\",lamb)\n",
    "print(\"矩阵A的特征向量为：\\n\",p)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2bfa6f9d",
   "metadata": {},
   "source": [
    "在刚刚的讨论中，我们了解了一种十分神奇的向量叫特征向量，这个向量可以在某个矩阵的变换下保持在同一直线上，也就是没有发生角度的偏转。那好奇的我们又开始想问题了，有没有一个矩阵是可以做到令一个向量进行旋转变换或者镜像变换呢？仔细思考下可以发现，这两种变换并没有改变向量的长度，而刚刚的特征向量反而与原向量的关系是拉伸（缩短）的关系。那令一个向量进行旋转变换或者镜像变换的矩阵是什么呢？答案就是：**正交矩阵**。\n",
    "\n",
    "如果满足以下等式的矩阵$A$称为正交矩阵：\n",
    "$$\n",
    "A^TA = AA^T = I\n",
    "$$\n",
    "通过上式，我们很快能知道：正交矩阵的逆矩阵与转置矩阵相同，即：$A^{-1} = A^T$，因为：$A^{-1}A=I$。同时，正交矩阵有一个非常好的性质：A的各行是单位向量且两两正交（垂直），又或者说A的各列是单位向量且两两正交（垂直），为什么呢？为了说明这个性质，我们将矩阵$A$分成n个行向量或者n个列向量，即：\n",
    "$$\n",
    "A=\\left(\\begin{array}{c}\n",
    "\\alpha_{1} \\\\\n",
    "\\alpha_{2} \\\\\n",
    "\\vdots \\\\\n",
    "\\alpha_{n}\n",
    "\\end{array}\\right)=\\left(\\beta_{1}, \\beta_{2}, \\cdots, \\beta_{n},\\right)\n",
    "$$\n",
    "\n",
    "因此，我们可以得到以下规律：\n",
    "   - $\\alpha_{i} \\cdot \\alpha_{i}^{T}=1$，也就是说$\\alpha_{i} $是单位向量。\n",
    "   - $\\alpha_{i} \\cdot \\alpha_{j}^{T}=0 \\quad(i \\neq j)$，向量之间两两正交。\n",
    "\n",
    "说到这里，已经有人能看出来，最简单的一个正交矩阵是单位矩阵，我们可以将它想象成一个坐标轴，而别的正交矩阵可以由这个坐标轴绕着原点进行旋转或者镜像得到，如图：\n",
    "![jupyter](./figures/2-4.png)\n",
    "\n",
    "到现在为止，我们已经很显然发现了一个结论：$det(A) = 1$或者$-1$，因为正交矩阵可以由坐标轴组成的正方体旋转或者镜像变换而来，行列式的绝对值描述了向量围成的面积/体积，因此正交矩阵的行列式要么是1，要么是-1。如果是数学推导的话，即：\n",
    "$$\n",
    "\\begin{aligned}\n",
    "&1=\\operatorname{det}(I)=\\operatorname{det}\\left(A^{T} A\\right)=\\operatorname{det}\\left(A^{T}\\right) \\operatorname{det}(A)=\\operatorname{det}(A)^{2} \\\\\n",
    "&\\Rightarrow \\operatorname{det}(A)=\\pm 1\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "因此给定一组基，我们怎么把他变成标准正交基呢？这里面用到的工具叫**施密特正交化(Gram-Schmidt)**，原理就是：我随便找一个原向量，把它固定住，接着找来第二个向量，往上面做投影，剩下的垂直分量就是第二个正交基，·····重复的做下去，直到所有基都变换过一遍后，得到的这组新的基就是正交基. 更进一步，如果我们把所有基进行标准化，使得每个基自己与自己做内积都为1，即模长为1，则得到的是一组标准正交基. 正交矩阵就为一个单位矩阵，就跟我们上面的解释完全吻合了. 下面给出施密特正交化的Pyhton代码： \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "ee043e18",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-05-27T16:37:59.282577Z",
     "start_time": "2022-05-27T16:37:59.272565Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.00000000e+00 -2.77731144e-16 -8.56351296e-17]\n",
      " [-2.77731144e-16  1.00000000e+00 -2.10355992e-16]\n",
      " [-8.56351296e-17 -2.10355992e-16  1.00000000e+00]]\n",
      "[[1. 0. 0.]\n",
      " [0. 1. 0.]\n",
      " [0. 0. 1.]]\n"
     ]
    }
   ],
   "source": [
    "# 施密特正交化(Gram-Schmidt)\n",
    "from scipy.linalg import *\n",
    "A = np.array([[1,2,3],\n",
    "              [2,1,3],\n",
    "              [3,2,1]])\n",
    "B = orth(A)  # 正交化，奇异值分解不是施密特正交化\n",
    "print(np.matmul(B,np.transpose(B)))   # 输出单位矩阵\n",
    "\n",
    "# 数值过滤\n",
    "res = np.matmul(B,np.transpose(B))\n",
    "res[np.abs(res) <1e-6] = 0 # 将绝对值小于10的-6次方的值设为0\n",
    "print(res)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "58aba600",
   "metadata": {},
   "source": [
    "有了这些工具后，我们终于可以给Ginger家的智慧农场做点不一样的事情了.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6ce20ac7",
   "metadata": {},
   "source": [
    "## 项目实战——基于矩阵变换的图像变换"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "afd1d751",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-info\" role=\"alert\">\n",
    "❓ 由于某些原因，Ginger发现家里的摄像头拍出来的图片是“倒了”的影像，但作为一个技术从业人员，她认为能用钱解决的事情一定不要用钱去解决. 因此她决定自己动手写一个小程序将这些图片恢复正常.\n",
    "</div>\n",
    "\n",
    "<img src=\"./figures/2-6.jpg\" width = \"200\" height = \"400\" div align=center />"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ad03a168",
   "metadata": {},
   "source": [
    "我们先来看看每个点是怎么旋转的，首先我们建立一个平面直角坐标系，来观察向量的变换.\n",
    "\n",
    "<img src=\"./figures/2-7.png\" width = \"400\" height = \"400\" div align=center />\n",
    "\n",
    "我们给定一个向量$u=(3,2)$，将其逆时针旋转$90^{\\circ}$，可以得到向量$v=(-2,3)$.\n",
    "\n",
    "设初始向量$u=(x,y)$，逆时针旋转的角度为$\\alpha$. 此时可以推出，\n",
    "$$\n",
    "\\theta = \\arctan{\\frac{y}{x}} \\\\\n",
    "r = ||u||_2\n",
    "$$\n",
    "旋转后得到的坐标为\n",
    "$$\n",
    "x' = r\\cos{(\\theta - \\alpha)}\\\\\n",
    "y' = r\\sin{(\\theta - \\alpha)}\n",
    "$$\n",
    "利用三角和差公式得\n",
    "$$\n",
    "\\cos{(\\theta - \\alpha)} = \\cos{\\theta} \\cos{\\alpha}+\\sin{\\theta}\\sin{\\alpha}\\\\\n",
    "\\sin{(\\theta - \\alpha)} = \\sin{\\theta}\\cos{\\alpha} - \\cos{\\theta}\\sin{\\alpha}\n",
    "$$\n",
    "则\n",
    "$$\n",
    "\\begin{aligned}\n",
    "x' &= r\\cos{\\theta} \\cos{\\alpha}+ r\\sin{\\theta}\\sin{\\alpha}\\\\\n",
    "&= x \\cos{\\alpha} + y \\sin{\\alpha}\\\\\n",
    "y' &= r\\sin{\\theta}\\cos{\\alpha} - r\\cos{\\theta}\\sin{\\alpha}\\\\\n",
    "&= y \\cos{\\alpha} - x \\sin{\\alpha}  \n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "<div class=\"alert alert-warning\" role=\"alert\">\n",
    "<h4>📋任务</h4> \n",
    "\n",
    "请你根据上式，补全下面矩阵中的问号处\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d261c72b",
   "metadata": {},
   "source": [
    "上面的式子(38)可以用矩阵形式表达：\n",
    "$$\n",
    "\\left[\\begin{array}{lll} \n",
    "x' & y' & 1\n",
    "\\end{array}\\right]=\\left[\\begin{array}{lll} \n",
    "x  & y  & 1\n",
    "\\end{array}\\right]\\left[\\begin{array}{ccc}\n",
    "? & ? & 0 \\\\\n",
    "? & ? & 0 \\\\\n",
    "0 & 0 & 1\n",
    "\\end{array}\\right]\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "646524c9",
   "metadata": {},
   "source": [
    "同理，我们可以根据公式(38)计算得到原坐标$(x,y)$关于变换后坐标的表达式:\n",
    "$$\n",
    "\\left[\\begin{array}{lll}\n",
    "x & y & 1\n",
    "\\end{array}\\right]=\\left[\\begin{array}{lll}\n",
    "x' & y' & 1\n",
    "\\end{array}\\right]\\left[\\begin{array}{ccc}\n",
    "\\cos \\alpha & \\sin \\alpha & 0 \\\\\n",
    "-\\sin \\alpha & \\cos \\alpha & 0 \\\\\n",
    "0 & 0 & 1\n",
    "\\end{array}\\right]\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5db6c59b",
   "metadata": {},
   "source": [
    "下面我们来尝试用python实现对二维向量的旋转："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "d3ef3e34",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-06-02T16:11:49.666070Z",
     "start_time": "2022-06-02T16:11:49.647058Z"
    }
   },
   "outputs": [],
   "source": [
    "# 在------------位置补全代码\n",
    "import numpy as np\n",
    "from math import cos, sin, pi\n",
    "\n",
    "def vec_2d(x0, y0, alpha):\n",
    "    \"\"\"\n",
    "    旋转2维向量.\n",
    "    x0: 横坐标.\n",
    "    y0: 纵坐标.\n",
    "    alpha: 旋转角度，弧度制.\n",
    "    return:(x,y) 旋转后的坐标.\n",
    "    \"\"\"\n",
    "    origin = np.array([[x0, y0, 1]])\n",
    "    Trans = np.array([[cos(alpha), -sin(alpha), 0],\n",
    "                      [sin(alpha), cos(alpha), 0],\n",
    "                      [0, 0, 1]])\n",
    "    \n",
    "    res =   origin.dot(Trans)\n",
    "    x = # ------------\n",
    "    y = # ------------\n",
    "    return (x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "a26991a3",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-06-02T09:37:02.632047Z",
     "start_time": "2022-06-02T09:37:02.623072Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2.0, -3.0)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 运行效果应该如下\n",
    "vec_2d(3, 2, pi/2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2d03df09",
   "metadata": {},
   "source": [
    "但如果这样的话，会出现一个问题，对于一张图片而言，旋转中心在左上角，导致整张图片旋转不是中心旋转的. 下面我们需要对坐标轴进行平移，完善我们的变换公式"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e6489aca",
   "metadata": {},
   "source": [
    "<img src=\"./figures/2-8.png\">"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e40e32a1",
   "metadata": {},
   "source": [
    "假设图片宽度为$W$，高度为$H$，则在第一个坐标系下(左图)的坐标$(x',y')$，变换之后的坐标为$(x'',y'')$，则\n",
    "$$\n",
    "\\begin{aligned}\n",
    "x'' &= x'- \\frac{1}{2}W \\\\\n",
    "y'' &= -y'+ \\frac{1}{2}H\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "则对应的矩阵表示为：\n",
    "\n",
    "<div class=\"alert alert-warning\" role=\"alert\">\n",
    "<h4>📋任务</h4> \n",
    "\n",
    "请你根据上式，补全下面矩阵中的问号处\n",
    "</div>\n",
    "\n",
    "$$\n",
    "\\left[\\begin{array}{lll}\n",
    "x'' & y'' & 1\n",
    "\\end{array}\\right]=\\left[\\begin{array}{lll}\n",
    "x' & y' & 1\n",
    "\\end{array}\\right]\\left[\\begin{array}{ccc}\n",
    "? & ? & 0 \\\\\n",
    "? & ? & 0 \\\\\n",
    "? & ? & 1\n",
    "\\end{array}\\right]\n",
    "$$\n",
    "\n",
    "同理可以求得其逆变换矩阵为：\n",
    "$$\n",
    "\\left[\\begin{array}{lll} \n",
    "x _{0} & Y _{0} & 1\n",
    "\\end{array}\\right]=\\left[\\begin{array}{lll} \n",
    "x & y & 1\n",
    "\\end{array}\\right]\\left[\\begin{array}{ccc}\n",
    "1 & 0 & 0 \\\\\n",
    "0 & -1 & 0 \\\\\n",
    "-0.5 W & 0.5 H & 1\n",
    "\\end{array}\\right]\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e41d8976",
   "metadata": {},
   "source": [
    "根据图像旋转的一般过程：\n",
    "1. 将原始图像的坐标系转换为数学坐标系；\n",
    "2. 通过旋转公式对冬像坐标进行旋转；\n",
    "3. 将旋转后的数学坐标系转换为图像坐标系.\n",
    "\n",
    "因此图像旋转的矩阵变换为：\n",
    "$$\n",
    "\\left[\\begin{array}{lll} \n",
    "x'' & y'' & 1\n",
    "\\end{array}\\right]=\\left[\\begin{array}{lll} \n",
    "x & y & 1\n",
    "\\end{array}\\right]\\left[\\begin{array}{ccc}\n",
    "1 & 0 & 0 \\\\\n",
    "0 & -1 & 0 \\\\\n",
    "-0.5 W & 0.5 H & 1\n",
    "\\end{array}\\right]\\left[\\begin{array}{ccc}\n",
    "\\cos \\alpha & -\\sin \\alpha & 0 \\\\\n",
    "\\sin \\alpha & \\cos \\alpha & 0 \\\\\n",
    "0 & 0 & 1\n",
    "\\end{array}\\right]\\left[\\begin{array}{ccc}\n",
    "1 & 0 & 0 \\\\\n",
    "0 & -1 & 0 \\\\\n",
    "0.5 W & 0.5H & 1\n",
    "\\end{array}\\right]\\\\\n",
    "=\\left[\\begin{array}{lll} \n",
    "x & y & 1\n",
    "\\end{array}\\right] \\left[\\begin{array}{ccc}\n",
    "\\cos \\alpha & \\sin \\alpha & 0 \\\\\n",
    "-\\sin \\alpha & \\cos \\alpha & 0 \\\\\n",
    "-0.5 W \\cos \\alpha +0.5 H \\sin \\alpha +0.5W & -0.5W \\sin \\alpha -0.5 H \\cos \\alpha + 0.5 H & 1\n",
    "\\end{array}\\right]\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "id": "36d42410",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-06-02T18:04:29.873112Z",
     "start_time": "2022-06-02T18:04:29.863165Z"
    }
   },
   "outputs": [],
   "source": [
    "# 图像旋转的矩阵\n",
    "def Trans(x0, y0, W, H, alpha):\n",
    "    origin = np.array([[x0, y0, 1]])\n",
    "    res = origin.dot(np.array([[cos(alpha), sin(alpha), 0],\n",
    "                     [-sin(alpha), cos(alpha), 0],\n",
    "                     [-0.5*W*cos(alpha) + 0.5*H*sin(alpha) + 0.5*W, -0.5*W*sin(alpha) - 0.5*H*cos(alpha) + 0.5*H, 1]]))\n",
    "    return (int(res[0,:2][0]),int(res[0,:2][1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "id": "19404de5",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-06-02T18:04:31.664737Z",
     "start_time": "2022-06-02T18:04:31.386481Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(328, 400)"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAVQAAAEYCAYAAAADCA6iAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAAsTAAALEwEAmpwYAAAWC0lEQVR4nO3df4xlZX3H8fenC6wGiIBMN9vdTVntNgSbutApxWiMlVhh/1lMKFn/0I0hWdNCoolNumhSMamJNlUSkxazBspqrUD9ETYNbV2RxPiHwIDLsj9ERn5kd7LsjiKINcWC3/5xn2GPw525v86P55z7eSU3c+5zzp37vec853Ofc869M4oIzMxscr/TdAFmZl3hQDUzK4kD1cysJA5UM7OSOFDNzEriQDUzK0llgSrpKkmPS5qXtLuq5zEzy4Wq+ByqpDXAj4H3AMeBh4D3R8SR0p/MzCwTVY1QLwfmI+LJiPg1cCewvaLnMjPLwhkV/d4NwLHC/ePAnxUXkLQL2AVw9tln/8nFF19cUSlmZuV5+OGHfxoRM/3mVRWoA0XEHmAPwOzsbMzNzTVVipnZ0CQ9s9K8qg75F4BNhfsbU5uZWWdVFagPAVskbZZ0FrAD2FfRc5mZZaGSQ/6IeFnSjcB/A2uA2yPicBXPZWaWi8rOoUbEvcC9Vf1+M7Pc+JtSZmYlcaCaWZYkjdSeAweqmWWnjWEKDlQzy0xbwxQa/GC/mVnR8sAs/p2RNoQpeIRqZhkYJTBz/seiDlQza1RbRp/D8CG/mTVmUJi2LWwdqGZWqXFDsW1hCg5UMytBG8OvCg5UMxta08GZ8wUpcKCa2QBNh2ib+Cq/ma0opzDNfXQKHqGaWUFOAbqcpOxD1SNUMwPyDtMludfoQDWz7IOqLXzIbzal2hqiS3XnePjvEarZFGprmBbl+BocqGZTJscg6gof8ptNga6GaG6H/x6hmlnr5fKG4UA167hcwmYaOFDNOkrSVIVpDq/VgWrWQTmEyzRyoJp1zDSHadOv3YFq1iFNB8q0c6CadYTDtHkOVLMOcJie1uS6cKCatZzDNB8TfVNK0tPAi8ArwMsRMSvpAuAu4CLgaeC6iPj5ZGWaWT8O07yUMUL984jYGhGz6f5u4L6I2ALcl+6bWckcpvmp4pB/O7A3Te8FrqngOcymmsN0dU2tn0kDNYBvS3pY0q7Uti4iTqTpZ4F1/R4oaZekOUlzi4uLE5ZhZta8Sf/a1DsiYkHS7wL7Jf2oODMiQlLfPwMTEXuAPQCzs7N5/KkYsxbw6DRfE41QI2Ih/TwFfAu4HDgpaT1A+nlq0iLNbPq+mz+pJtbV2IEq6WxJ5y5NA38BHAL2ATvTYjuBeyYt0sxsHHWH6iSH/OuAb6WCzwD+LSL+S9JDwN2SrgeeAa6bvEwzs/yNHagR8STw1j7tPwOunKQoMzvNh/nt4W9KmWXMYTq5OtehA9XMrCQOVLNMeXRanrrWpQPVLEMO0/LVsU4dqGaZcZi2lwPVzKwkDlSzjHh0Wq2q168D1SwTDtP2c6CaZcBhWp8q/yaCA9XMShcxnX9AzoFq1rCujk6nMVQn/XuoZjamaQjSfqGay+uWVHroe4RqZrXq8sjVgWpmtYuIV29NKnu07EN+s5rlcshbhXECcvlj6l4/ZR76e4RqVqMuh2lZchi5jsuBalYTh+lo2hiqPuRvobJ3zDZ23DaZliCtoh8t/c6q1+HS75/0NThQM1bXjrj8eRyw5ZiWIK1DRLRifTpQM5NDp3HATi6H7VinOvpIHaE66QUqB2pD2rTDrVSrg/a0Nm3PNqvrFMC4HKg1yrUTjKv4eqY1XLu2Tdsi11MADtQS5biB6zJNpwmmeTvb6hyoK/BOM5nV1l9bwtZ9IG9VjFJ9lb9E3oHq0W89Nxmy3u6TaXLblRmqZbwOByreoXJQ5YjW29fqMrWB6p2sPbytbDVljFL9Xf4JeAc1K0cu58MnqaPM1zAwUCXdLumUpEOFtgsk7Zf0RPp5fmqXpC9Impd0UNJlpVVaEoepmVVlmBHqHcBVy9p2A/dFxBbgvnQf4GpgS7rtAm4tp8zJVfmPucysnWr/i/0R8T3guWXN24G9aXovcE2h/cvR8wPgPEnrS6rVzDKSy+H+klHrqaL+cc+hrouIE2n6WWBdmt4AHCssdzy1vYakXZLmJM0tLi6OWcZwPDI1szpMfFEqejE/ctRHxJ6ImI2I2ZmZmUnL6KvKw/xc/oWDmZ1W3CeL+2i/WxXGDdSTS4fy6eep1L4AbCostzG1mZnVpqmBzriBug/YmaZ3AvcU2j+YrvZfAbxQODXQGR6Vmlk/Az/YL+lrwLuACyUdBz4JfAa4W9L1wDPAdWnxe4FtwDzwK+BDFdQ8UJXnTJv+h2Jmlq+BgRoR719h1pV9lg3ghkmLaguHqZkVde6bUg45s+r5tFd/nQvUKhU7kYPbzJZzoJqZlcSBOiSPTs16fLi/sk4Fah1B5zA1s5V0KlCr4ndksx7vC6vrTKB65GhmTetMoJqZNa0TgVrX6NSjYJtmPtwfrBOBamaWAwfqAH5XNvN+MCwHqplZSRyoZrYqj06H50Adki9ImdkgDlQzs5K0PlA9cjSzXLQ+UM3McuFANTMriQPVzKwkrQ7Uqs+f+uMiZjaKVgdqnRyuZjaIA9XMrCQOVDOzkjhQzcxK4kA1MyuJA9XMVuSLsaNpbaD6K6dmlpvWBmoT/G5tZqtxoJqZlWRgoEq6XdIpSYcKbTdLWpB0IN22FebdJGle0uOS3ltV4WZmuRlmhHoHcFWf9lsiYmu63Qsg6RJgB/CW9Jh/lrSmrGLNzHI2MFAj4nvAc0P+vu3AnRHxUkQ8BcwDl09Qn5lZa0xyDvVGSQfTKYHzU9sG4FhhmeOp7TUk7ZI0J2lucXFxgjLMzPIwbqDeCrwZ2AqcAD436i+IiD0RMRsRszMzM2OWUT9f6bdp4b4+urECNSJORsQrEfEb4EucPqxfADYVFt2Y2szMOm+sQJW0vnD3fcDSJwD2ATskrZW0GdgCPDhZiWZm7XDGoAUkfQ14F3ChpOPAJ4F3SdoKBPA08GGAiDgs6W7gCPAycENEvFJJ5Q2KCH9Ty8xeQzmcJ5mdnY25ubmRHlNHoK22bhyo1nU5ZEOOJD0cEbP95vmbUmNyZzOz5RyoZvYaHjCMx4FqZlYSB6qZWUkcqGZmJXGgTsDnmcysyIFqffnNwmx0DtQJdTF4ll5TRLx6M7PBBn5TyqbHasG5fJ6/2NBdfgMdn0eoJehCBxz1NXThNZuVzYFqY/PpALPf5kN+mzgUi4/3qYD28pvj5DxCtVJ5p7Rp5kCdclUEoE8F2LRyoJakjQFSdc3+2FV7eBuVw4FqtfAOmy9vm/I4UFfgTlY+j1bz4+1RLl/ln1JN7kj9ntufDqifw7R8HqGWyB10fD7fWi+v52p4hDqFct+Z/DXXauW+/dvMgTpl2rgzjVqzA9ia4kC1zhn3TcNBbJNyoJolk47eHcjmQDUryTCB3HTotvGUT5v4Kn+Jmt5ZBvHOZFYtB6qZWUkcqFPCo1NzH6ieA7UkuR/um1n1BgaqpE2S7pd0RNJhSR9J7RdI2i/pifTz/NQuSV+QNC/poKTLqn4RZmY5GGaE+jLwsYi4BLgCuEHSJcBu4L6I2ALcl+4DXA1sSbddwK2lV20j8aGeuQ/UY2CgRsSJiHgkTb8IHAU2ANuBvWmxvcA1aXo78OXo+QFwnqT1ZRduZpabkc6hSroIuBR4AFgXESfSrGeBdWl6A3Cs8LDjqW3579olaU7S3OLi4qh1Z8XnT80MRghUSecA3wA+GhG/KM6L3vHESMcUEbEnImYjYnZmZmaUh2bFYWpmS4YKVEln0gvTr0bEN1PzyaVD+fTzVGpfADYVHr4xtVkDfO7MrD7DXOUXcBtwNCI+X5i1D9iZpncC9xTaP5iu9l8BvFA4NdApHp1aG/hNtT7DfJf/7cAHgMckHUhtHwc+A9wt6XrgGeC6NO9eYBswD/wK+FCZBXfdUucvI6y9I5nVa2CgRsT3gZX27iv7LB/ADRPWlb2yR6cOP6uC+1W9/E2pMVQdpj6VYNZODtQRtWVk6pFJnrxdus2B2kddnd47l1XJ/at+DtQRlDk6Xamz+3DfrL38F/uXqeN/xnvkML38htltHqHWzGFq1l0OVDOzkviQv6Dqjy/5YpfVxX2gGR6h1sQd3Kz7WhuoVQdUHVf0zarg/tac1gZqW7hzm00PB2rHOMCnm7d/sxyoZmYl8VX+inikYDZ9PEJNHIBmNikHagUmCWcHu1l7tTpQi+HTpSAa97V0aR2YtVGrA7UsZQaRQ81sejlQM+VgNmuf1gdqTsGTUy02fdz/mtf6QIU8LgK5M5tZJwK1qxzSZu3iQM2cQ9WsPToZqCuFkP/DqJlVqZOB2jUObBvEfSQPUx2oZXRCd2QzW9K5QHXAmVlTOheodXJ4Ww7cD/MxMFAlbZJ0v6Qjkg5L+khqv1nSgqQD6bat8JibJM1LelzSe6t8AUWrfbc/Il79tyYR4U5oZqUb5u+hvgx8LCIekXQu8LCk/WneLRHxj8WFJV0C7ADeAvwe8B1JfxgRr5RZuJlZbgaOUCPiREQ8kqZfBI4CG1Z5yHbgzoh4KSKeAuaBy8sotgxtHZm2tW6zaTLSOVRJFwGXAg+kphslHZR0u6TzU9sG4FjhYcdZPYBr478qZU0a9j/pum+119CBKukc4BvARyPiF8CtwJuBrcAJ4HOjPLGkXZLmJM0tLi6O8lAzsywNFaiSzqQXpl+NiG8CRMTJiHglIn4DfInTh/ULwKbCwzemtt8SEXsiYjYiZmdmZiZ5DStauvjkd3xri1H7qvt2Xoa5yi/gNuBoRHy+0L6+sNj7gENpeh+wQ9JaSZuBLcCD5ZXcPHdiM+tnmKv8bwc+ADwm6UBq+zjwfklbgQCeBj4MEBGHJd0NHKH3CYEbfIW/HMWPfln3+I26/QYGakR8H+i3F9+7ymM+DXx6grrMbAAHcH78TSmzDDks28mBapYBX4zqBgeqmVlJHKgd4gtW+fK2mQ4O1JbxoZ5ZvhyoI3KgmdlKHKgd40NLs+Y4UM3MSuJA7aPto7y212/WVg5UM7OSOFDNKuYjhunhQDUzK4kDdZmujCa68jrstfzRvXw5UM0y5eBsHwdqCw27o3mUalYvB2pBFwOoi69p2nmb5suBamZWEgeqmVlJHKgt5QsWZvlxoE4Bn3Mzq4cD1cysJA7UZNhRXE6jvVEO+yVlVbtZFzlQW87nUs3y4UDtgFFHqmZWDQfqGHI8fI6Ikb5BlVv9Nhpvvzw5UDvGpwDMmuNATcYJoraPEtpev1luHKgFS4fNbb963vb6p9E428DbLT8O1BWMGqxmk3Kott/AQJX0OkkPSnpU0mFJn0rtmyU9IGle0l2Szkrta9P9+TT/oopfQxba3rHbXn/O/MY8PYYZob4EvDsi3gpsBa6SdAXwWeCWiPgD4OfA9Wn564Gfp/Zb0nJTIafD52k8J5yzYY94lm+DYR/jbZeHgYEaPb9Md89MtwDeDXw9te8FrknT29N90vwr5a3dGt5UzRsnVPs9zuo31DlUSWskHQBOAfuBnwDPR8TLaZHjwIY0vQE4BpDmvwC8sc/v3CVpTtLc4uLiRC/CrGvGDVVr1lCBGhGvRMRWYCNwOXDxpE8cEXsiYjYiZmdmZib9dVnJZaTgC2vtNu5FKp8CaM5IV/kj4nngfuBtwHmSzkizNgILaXoB2ASQ5r8B+FkZxbZJWzu0Azgvbe1H02qYq/wzks5L068H3gMcpRes16bFdgL3pOl96T5p/ndjSvfSXHaGYT9fO6WbqTVG3T659L9pcsbgRVgP7JW0hl4A3x0R/yHpCHCnpL8Hfgjclpa/DfiKpHngOWBHBXXXJiI61TEdmu2z1P8m+eSGt3s9BgZqRBwELu3T/iS986nL2/8X+MtSqstE10LVpo8kh2oN/E2pIbkzWhnG6UfF0zXuh3kb5pDfkqXO7NGqTcKh2F0O1DEUdwh/XtDq5lNQ+XKgTsgBarlzH62PA9WshRySefJFKTOzkjhQzcxK4kA1MyuJA9XMrCQOVDOzkjhQzcxK4kA1MyuJA9XMrCQOVDOzkjhQzcxKohy+wiZpEfgf4KdN17LMhbimYeVYV441QZ515VgT5FnX70dE33+El0WgAkiai4jZpusock3Dy7GuHGuCPOvKsSbIt66V+JDfzKwkDlQzs5LkFKh7mi6gD9c0vBzryrEmyLOuHGuCfOvqK5tzqGZmbZfTCNXMrNUcqGZmJWk8UCVdJelxSfOSdjdcy9OSHpN0QNJcartA0n5JT6Sf51dcw+2STkk6VGjrW4N6vpDW3UFJl9Vc182SFtL6OiBpW2HeTamuxyW9t6KaNkm6X9IRSYclfSS1N7a+Vqmp6XX1OkkPSno01fWp1L5Z0gPp+e+SdFZqX5vuz6f5F9VY0x2Sniqsq62pvbb+Pral//ndxA1YA/wEeBNwFvAocEmD9TwNXLis7R+A3Wl6N/DZimt4J3AZcGhQDcA24D8BAVcAD9Rc183A3/RZ9pK0LdcCm9M2XlNBTeuBy9L0ucCP03M3tr5WqanpdSXgnDR9JvBAWgd3AztS+xeBv0rTfw18MU3vAO6qsaY7gGv7LF9bfx/31vQI9XJgPiKejIhfA3cC2xuuabntwN40vRe4psoni4jvAc8NWcN24MvR8wPgPEnra6xrJduBOyPipYh4Cpint63LrulERDySpl8EjgIbaHB9rVLTSupaVxERv0x3z0y3AN4NfD21L19XS+vw68CVKvl/V69S00pq6+/jajpQNwDHCvePs3rnq1oA35b0sKRdqW1dRJxI088C6xqoa6Uaclh/N6bDr9sLp0Nqrysdkl5Kb5STxfpaVhM0vK4krZF0ADgF7Kc3Gn4+Il7u89yv1pXmvwC8seqaImJpXX06ratbJK1dXlOferPQdKDm5h0RcRlwNXCDpHcWZ0bvuKPRz5nlUEPBrcCbga3ACeBzTRQh6RzgG8BHI+IXxXlNra8+NTW+riLilYjYCmykNwq+uO4alltek6Q/Am6iV9ufAhcAf9tchaNpOlAXgE2F+xtTWyMiYiH9PAV8i16nO7l0WJF+nmqgtJVqaHT9RcTJtEP8BvgSpw9Va6tL0pn0guurEfHN1Nzo+upXUw7raklEPA/cD7yN3mHzGX2e+9W60vw3AD+roaar0mmTiIiXgH+hwXU1qqYD9SFgS7rSeBa9k9/7mihE0tmSzl2aBv4COJTq2ZkW2wnc00B5K9WwD/hguvp5BfBC4VC3csvOX72P3vpaqmtHulK8GdgCPFjB8wu4DTgaEZ8vzGpsfa1UUwbrakbSeWn69cB76J3fvR+4Ni22fF0trcNrge+m0X7VNf2o8GYoeud0i+uqsf4+lKavitG7cvdjeudzPtFgHW+id7X1UeDwUi30zhvdBzwBfAe4oOI6vkbvkPD/6J0jun6lGuhd7fyntO4eA2Zrrusr6XkP0uvs6wvLfyLV9ThwdUU1vYPe4fxB4EC6bWtyfa1SU9Pr6o+BH6bnPwT8XaHfP0jvYti/A2tT++vS/fk0/0011vTdtK4OAf/K6U8C1Nbfx735q6dmZiVp+pDfzKwzHKhmZiVxoJqZlcSBamZWEgeqmVlJHKhmZiVxoJqZleT/ARadBLZE1CbKAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from skimage import io, data\n",
    "img3 = data.horse()\n",
    "io.imshow(img3)\n",
    "img3.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "id": "bee0f909",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-06-02T18:04:37.505039Z",
     "start_time": "2022-06-02T18:04:35.078456Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x2048cedce50>"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "img4 = np.zeros((400, 400))\n",
    "\n",
    "for x in range(img3.shape[0]):\n",
    "    for y in range(img3.shape[1]):\n",
    "        x1, y1 = Trans(x, y, 328, 400, pi/2)\n",
    "        img4[x1-355, y1] = img3[x, y] # 335是做了一步平移居中，保证画面完整性\n",
    "io.imshow(img4)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "92d44873",
   "metadata": {},
   "source": [
    "以上，我们理论出发，手把手带着你复现了图像旋转的流程，相信在这个过程中，你已经深刻的体会到了从理论，如何被应用到实际当中！当然，我们的实现过程是比较粗糙的，简单粗暴的！当你理解了一个理论工具后，如果你还将它实现了，更好的方式是把它封装成一个函数，放到你的代码库中，方便日后的使用！\n",
    "\n",
    "当然现在Python有很多现成的工具库，可以实现图像旋转的功能，例如```skimage```——一个图像处理库.\n",
    "\n",
    "<div class=\"alert alert-warning\" role=\"alert\">\n",
    "<h4>📋任务</h4> \n",
    "\n",
    "下面请你学习使用```skimage```内置函数```transform.rotate```，尝试一键旋转Ginger的农场里的小鸡！\n",
    "</div>\n",
    "\n",
    "文档地址：\n",
    "[transform.rotate](https://scikit-image.org/docs/stable/api/skimage.transform.html?highlight=transform%20rotate#skimage.transform.rotate)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "d915edba",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-06-10T18:35:35.001739Z",
     "start_time": "2022-06-10T18:35:13.707923Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x21580031580>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from skimage import io, transform\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "dirpath = \"./figures/2-6.jpg\"\n",
    "img = io.imread(dirpath) #读取数据\n",
    "plt.imshow(img) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "010deb5f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 在#------------位置补全代码\n",
    "# 旋转图像\n",
    "img2 = #------------\n",
    "plt.imshow(img2) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "id": "106d358d",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-06-02T17:56:40.536564Z",
     "start_time": "2022-06-02T17:56:35.906010Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x2048d277040>"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 不要运行本代码块！！！\n",
    "# 请保证运行完是如下结果"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "79e17d6f",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-success\" role=\"alert\">\n",
    "  <h4 class=\"alert-heading\">Well done!</h4>\n",
    "  <p>恭喜你，完成了《线性代数》的学习，希望在日后的数模竞赛中，通过本课程的学习，你可以更加深刻的理解矩阵的强大之处，以及更多的使用向量化编程，提高代码的运行效率.</p>\n",
    "  <hr>\n",
    "  <p class=\"mb-0\">如有需要领取本次组队学习的答案，敬请关注公众号以及留意直播讲解！</p>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3b3f46aa",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "author": "me",
  "kernelspec": {
   "display_name": "ML38",
   "language": "python",
   "name": "ml38"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.12"
  },
  "latex_envs": {
   "LaTeX_envs_menu_present": true,
   "autoclose": false,
   "autocomplete": true,
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 1,
   "hotkeys": {
    "equation": "Ctrl-E",
    "itemize": "Ctrl-I"
   },
   "labels_anchors": false,
   "latex_user_defs": false,
   "report_style_numbering": false,
   "user_envs_cfg": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
